We investigate the theoretical framework of the cos 2φ azimuthal asymmetry contributed by the coupling of two Boer-Mulders functions in the dilepton production unpolarized πp Drell-Yan process by applying the transverse momentum dependent factorization at leading order. We adopt the model calculation results of the unpolarized distribution function f1 and Boer-Mulders function h ⊥ 1 of pion meson from the light-cone wave functions. We take into account the transverse momentum evolution effects for both the distribution functions of pion and proton by adopting the existed extraction of the nonperturbative Sudakov form factor for the pion and proton distribution functions. An approximate kernel is included to deal with the energy dependence of the Boer-Mulders function related twist-3 correlation function T (σ) q,F (x, x) needed in the calculation. We numerically estimate the Boer-Mulders asymmetry νBM as the functions of xp, xπ, xF and qT considering the kinematics at COMPASS Collaboration. 13.85.Qk, 13.88.+e
I. INTRODUCTIONThe Boer-Mulders function is a transverse momentum dependent (TMD) parton distribution function (PDF) that describes the transverse-polarization asymmetry of quarks inside an unpolarized hadron [1,2]. Arising from the correlation between the quark transverse spin and the quark transverse momentum, the Boer-Mulders function manifests novel spin structure of hadrons [3]. For a while the very existence of the Boer-Mulders function was not as obvious. This is because, similar to its counterpart, the Sivers function, the Boer-Mulders function was thought to be forbidden by the time-reversal invariance of QCD [4]. For this reason, they are classified as T-odd distributions. However, model calculations incorporating gluon exchange between the struck quark and the spectator [5,6], together with a re-examination [7] on the time-reversal argument, show that T-odd distributions actually do not vanish. It was found that the gauge-links [7][8][9][10] in the operator definition of TMD distributions play an essential role for a nonzero Boer-Mulders function.As a chiral-odd distribution, the Boer-Mulders function has to be coupled with another chiral-odd distribution/fragmentation function to survive in a high energy scattering process. Two promising processes for accessing the Boer-Mulders function are the Drell-Yan and the semi-inclusive deep inelastic scattering (SIDIS) processes. In the former case, the corresponding observables are the cos 2φ azimuthal angular dependence of the final-state dilepton, which is originated by the convolution of two Boer-Mulders functions from each hadron. This effect was originally proposed by Boer [1] to explain the violation of the Lam-Tung relation observed in πN Drell-Yan process[11], a phenomenon which cannot be understood from purely perturbative QCD effects [12][13][14]. Similar asymmetry was also observed in the pd and pp Drell-Yan processes, and the corresponding data were applied to extract the proton Boer-Mulders function [15][16][17][18]. Besides the parmater...